Research on sea surface temperature retrieval by the one-dimensional synthetic aperture microwave radiometer, 1D-SAMR
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Abstract: Due to the low spatial resolution of sea surface temperature (TS) retrieval by real aperture microwave radiometers, in this study, an iterative retrieval method that minimizes the differences between brightness temperature (TB) measured and modeled was used to retrieve sea surface temperature with a one-dimensional synthetic aperture microwave radiometer, temporarily named 1D-SAMR. Regarding the configuration of the radiometer, an angular resolution of 0.43° was reached by theoretical calculation. Experiments on sea surface temperature retrieval were carried out with ideal parameters; the results show that the main factors affecting the retrieval accuracy of sea surface temperature are the accuracy of radiometer calibration and the precision of auxiliary geophysical parameters. In the case of no auxiliary parameter errors, the greatest error in retrieved sea surface temperature is obtained at low TS scene (i.e., 0.710 6 K for the incidence angle of 35° under the radiometer calibration accuracy of 0.5 K). While errors on auxiliary parameters are assumed to follow a Gaussian distribution, the greatest error on retrieved sea surface temperature was 1.330 5 K at an incidence angle of 65° in poorly known sea surface wind speed (W) (the error on W of 1.0 m/s) over high W scene, for the radiometer calibration accuracy of 0.5 K.
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Figure 2. The variation of RMS error of retrieved sea surface temperature with the forward model, for various levels of noise. a. Approximately 0.25 K, b. approximately 0.50 K, and c. approximately 0.75 K on TB, with the incidence angle under five homogeneous scenes (Table 2).
Figure 3. The RMS error of retrieved sea surface temperature at different incidence angles over the five homogeneous scenes under nominal retrieval conditions (Table 4).
Figure 4. The RMS error on retrieved sea surface temperature at different incidence angles over the high TS scene (a, b), the low TS scene (c, d), the high W scene (e, f), and the low W scene (g, h), under different retrieval conditions.
Figure 5. The RMS error on retrieved sea surface temperature at different incidence angles and wind speed over the high TS scene (a), and the low TS scene (b) under nominal retrieval conditions (Table 4).
Table 1. Parameters of the one-dimensional synthetic aperture radiometer, 1D-SAMR
Parameters Values Frequency 6.9 GHz Bandwidth 200 MHz Polarization modes vertical and horizontal polarization Integral time 0.5 s Number of antenna elements 55 Minimum spacing of antenna elements $0.73 {\lambda _0}$ Angle range of field of view –43° to 43° Angle resolution 0.43° Size of parabolic cylindrical antenna 12 m × 10 m Spatial resolution along the swath 5 km 
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Table 2. Geophysical parameter values for the five homogeneous scenes used in the retrievals
Scene S TS/K W/m·s–1 $\varphi $/(°) V/mm L/mm Reference 35 293 10 45 30 0.1 High TS 35 303 10 45 30 0.1 Low TS 35 283 10 45 30 0.1 High W 35 293 15 45 30 0.1 Low W 35 293 7 45 30 0.1
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Table 3. The RMS error of retrieved sea surface temperature at different incidence angles under different calibration accuracies
Scene Calibration accuracy θEIA = 35° θEIA = 40° θEIA = 45° θEIA = 50° θEIA = 55° θEIA = 60° θEIA = 65° Reference 0.25 K 0.309 5 K 0.303 6 K 0.295 3 K 0.283 9 K 0.269 0 K 0.250 2 K 0.228 0 K 0.50 K 0.618 5 K 0.606 8 K 0.590 1 K 0.567 3 K 0.537 5 K 0.500 2 K 0.455 6 K 0.75 K 0.926 5 K 0.909 0 K 0.884 0 K 0.849 9 K 0.805 3 K 0.749 4 K 0.682 8 K High TS 0.25 K 0.286 5 K 0.281 4 K 0.274 2 K 0.264 3 K 0.251 4 K 0.235 1 K 0.215 7 K 0.50 K 0.572 9 K 0.562 8 K 0.548 3 K 0.528 5 K 0.502 7 K 0.470 2 K 0.431 4 K 0.75 K 0.859 3 K 0.844 0 K 0.822 3 K 0.792 6 K 0.753 8 K 0.705 1 K 0.647 0 K Low TS 0.25 K 0.355 8 K 0.348 1 K 0.337 1 K 0.322 1 K 0.302 5 K 0.278 2 K 0.249 3 K 0.50 K 0.710 6 K 0.695 3 K 0.673 3 K 0.643 4 K 0.604 4 K 0.555 8 K 0.498 2 K 0.75 K 1.063 7 K 1.040 8 K 1.008 0 K 0.963 2 K 0.905 0 K 0.832 4 K 0.746 3 K High W 0.25 K 0.297 9 K 0.292 7 K 0.285 4 K 0.275 4 K 0.262 2 K 0.245 5 K 0.225 2 K 0.50 K 0.595 3 K 0.584 9 K 0.570 3 K 0.550 3 K 0.524 1 K 0.490 8 K 0.450 1 K 0.75 K 0.891 8 K 0.876 3 K 0.854 4 K 0.824 5 K 0.785 3 K 0.735 4 K 0.674 6 K Low W 0.25 K 0.314 1 K 0.308 0 K 0.299 1 K 0.287 1 K 0.271 4 K 0.251 8 K 0.228 7 K 0.50 K 0.627 7 K 0.615 4 K 0.597 8 K 0.573 7 K 0.542 4 K 0.503 3 K 0.457 1 K 0.75 K 0.940 2 K 0.921 8 K 0.895 5 K 0.859 5 K 0.812 5 K 0.754 1 K 0.685 0 K
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Table 4. Retrieval conditions tested over the five homogeneous scenes
Retrieval conditions Prior values Pi Uncertainties ${\sigma _{{P_i}}}$ Noise on auxiliary parameters Nominal ${P_{ {T_{\rm S}} } } = $286.7 K ${\sigma _{ {T_{\rm S}} } } = $11.9 K ${\sigma _W} =$0.5 m·s–1, ${\sigma_{\varphi}} = $20°, ${\sigma_V} =$0.5 mm, ${\sigma_L} = $0.01 mm $W$ perfectly/poorly known nominal nominal ${\sigma _W} = $0 m·s–1/1.0 m·s–1 all other $\sigma $: nominal $\varphi $ perfectly/poorly known nominal nominal ${\sigma_{\varphi}} =$0°/40°, all other $\sigma $: nominal $V$ perfectly/poorly known nominal nominal ${\sigma_V} =$0 mm/1.0 mm, all other $\sigma $: nominal $L$ perfectly/poorly known nominal nominal ${\sigma _L} =$0 mm/0.02 mm, all other $\sigma $: nominal
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Table 5. The RMS errors of sea surface temperature retrieval for the reference scene specified in Table 2 under the retrieval configurations (Table 4)
Retrieval conditions θEIA = 35° θEIA = 40° θEIA = 45° θEIA = 50° θEIA = 55° θEIA = 60° θEIA = 65° Nominal 1.029 5 K 1.015 2 K 0.989 1 K 0.940 9 K 0.867 3 K 0.771 8 K 0.666 6 K σW 0 m/s 0.630 6 K 0.620 8 K 0.606 3 K 0.585 6 K 0.558 0 K 0.523 7 K 0.484 6 K 1.0 m/s 1.740 0 K 1.716 6 K 1.669 2 K 1.577 0 K 1.431 2 K 1.239 7 K 1.025 9 K σφ 0° 1.029 8 K 1.015 6 K 0.989 6 K 0.941 6 K 0.868 3 K 0.772 6 K 0.665 3 K 40° 1.030 4 K 1.018 1 K 0.995 0 K 0.951 1 K 0.882 8 K 0.794 1 K 0.696 8 K σV 0 mm 1.029 5 K 1.015 2 K 0.989 1 K 0.940 8 K 0.867 1 K 0.771 5 K 0.666 1 K 1.0 mm 1.030 3 K 1.016 2 K 0.990 2 K 0.942 2 K 0.868 9 K 0.773 9 K 0.669 1 K σL 0 mm 1.022 5 K 1.007 5 K 0.980 4 K 0.930 9 K 0.855 5 K 0.757 9 K 0.650 1 K 0.02 mm 1.050 7 K 1.038 7 K 1.015 5 K 0.971 1 K 0.902 6 K 0.813 4 K 0.715 2 K
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